Applications - Pre-Algebra 8 and ATImrsdahlinmath.weebly.com/uploads/1/0/4/0/10405150/moving... ·...

Applications1. Ms. Chang’s class decides to use the Cool Tee’s company to make their

T-shirts. The following equation represents the relationship betweencost C and the number of T-shirts n.

C = 2n + 20

a. The class wants to buy 25 T-shirts from Cool Tee’s. Describe howyou can use a table and a graph to find the cost for 25 T-shirts.

b. Suppose the class has $80 to spend on T-shirts. Describe how youcan use a table and a graph to find the number of T-shirts the classcan buy.

c. Sophia writes the following equation in her notebook:

C = 2(15) + 20

What information is Sophia looking for?

d. Elisa uses the coordinates (30, 80) to find information about thecost of the T-shirts. What information is she looking for?

2. The following equations represent some walkathon pledge plans.

Plan 1: 14 = 2x

Plan 2: y = 3.5(10) + 10

Plan 3: 100 = 1.5x + 55

In each equation, y is the amount owed in dollars, and x is the numberof kilometers walked. For each equation:

a. Tell what information is unknown.

b. Describe how you could find the information.

3. Find the solution (the value of the variable for each equation).

a. y = 3(10) + 15 b. 24 = x + 2 c. 10 = 2x + 4

4. Consider the equation: y = 5x - 15.

a. Find y if x = 1. b. Find x if y = 50.

c. Describe how you can use a table or graph to answer parts (a) and (b).

Investigation 3 Solving Equations 57

For: Help with Exercise 3Web Code: ane-5303

7cmp06se_MS3.qxd 5/18/06 2:34 PM Page 57

For each situation in Exercises 5–8, find the number of coins in each pouch.

5.

6.

7.

8.

9. Rudo’s grandfather gives Rudo $5 and then 50¢ for each math questionhe answers correctly on his math exams for the year.

a. Write an equation that represents the amount of money that Rudoreceives during a school year. Explain what the variables andnumbers mean.

b. Use the equation to find the number of correct answers Rudo needsto buy a new shirt that costs $25. Show your work.

c. Rudo answered all 12 problems correctly on his first exam. How muchmoney is he assured of receiving for the year? Show your work.

10. For each equation, sketch a picture using pouches and coins, and thendetermine how many coins are in a pouch.

a. 3x = 12 b. 2x + 5 = 19

c. 4x + 5 = 2x + 19 d. x + 12 = 2x + 6

e. 3(x + 4) = 18

=

=

=

=

58 Moving Straight Ahead


11. For parts (a) and (b), find the mystery number and explain yourreasoning.

a. If you add 15 to 3 times the mystery number, you get 78. What is themystery number?

b. If you subtract 27 from 5 times the mystery number, you get 83.What is the mystery number?

c. Make up clues for a riddle whose mystery number is 9.

12. Use properties of equality and numbers to solve each equation for x.Check your answers.

a. 7 + 3x = 5x + 13 b. 3x - 7 = 5x + 13

c. 7 - 3x = 5x + 13 d. 3x + 7 = 5x - 13

13. Multiple Choice Which of the following is a solution to the equation11 = -3x - 10?

A. 1.3 B. C. -7 D. 24

14. Use properties of equality and numbers to solve each equation for x.Check your answers.

a. 3x + 5 = 20 b. 3x - 5 = 20

c. 3x + 5 = -20 d. -3x + 5 = 20

e. -3x - 5 = -20

15. Solve each equation. Check your answers.

a. 3(x + 2) = 12 b. 3(x + 2) = x - 18

c. 3(x + 2) = 2x d. 3(x + 2) = -15

16. Two students’ solutions to the equation 6(x + 4) = 3x - 2 are shown.Both students made an error. Find the errors and give a correct solution.

6(x + 4) = 3x – 2x + 4 = 3x – 2 – 6x + 4 = 3x – 8

x + 4 + 8 = 3x – 8 + 8x + 12 = 3x

12 = 2xx = 6

Student 1

6(x + 4) = 3x – 26x + 4 = 3x – 23x + 4 = –2

3x + 4 – 4 = –2 – 43x = –6

x = –2

Student 2

2 13


For: Multiple-Choice SkillsPractice

Web Code: ana-5354


17. Two students’ solutions to the equation 58.5 = 3.5x - 6 are shownbelow. Both students made an error. Find the errors and give a correctsolution.

For Exercises 18 and 19, use the equation y ≠ 4 – 3x.

18. Find y if

a. x = 4 b. x = -3 c. x = 2

d. x = e. x = 0

19. Find x when:

a. y = 0 b. y = 21

c. y = -15 d. y = 3.5

20. Explain how the information you found for Exercises 18 and 19 relatesto locating points on a line representing y = 4 - 3x.

21. Use the equation P = 10 - 2.5c.

a. Find P when c = 3.2. b. Find c when P = 85.

c. Describe how you can use a table or graph to answer parts (a) and (b).

22. Use the equation m = 15.75 + 3.2d.

a. Find m when:

i. d = 20 ii. d = 0 iii. d = 3.2

b. Find d when:

i. m = 54.15 ii. m = 0 iii. m = 100

2 43

58.5 = 3.5x – 658.5 – 6 = 3.5x

52.5 = 3.5x

Student 1

so, x = 15 so, x � 1.84

58.5 = 3.5x – 658.5 + 6 = 3.5x – 6 + 6

64.5 = 3.5x

Student 2

= x52.53.5

= x64.53.5

3.53.5




23. Forensic scientists can estimate a person’s height by measuring thelength of certain bones, including the femur, the tibia, the humerus, andthe radius.

The table below gives equations for the relationships between thelength of each bone and the estimated height of males and females.These relationships were found by scientists after much study and datacollection.

In the table, F represents the length of the femur,T the length of the tibia, H the length of the humerus,R the length of the radius, and h the person’s height.All measurements are in centimeters.

a. About how tall is a female if her femur is 46.2 centimeters long?

b. About how tall is a male if his tibia is 50.1 centimeters long?

c. Suppose a woman is 152 centimeters tall.About how long is her femur? Her tibia? Her humerus? Her radius?

d. Suppose a man is 183 centimeters tall. About how long is his femur? His tibia? His humerus? His radius?

e. Describe what the graphs would look like for each equation. What do the x- and y-intercepts represent in this problem? Does this make sense? Why?

Humerus

Radius

Femur

Tibia

Bone

Femur

Tibia

Humerus

Radius

Male

h � 69.089 � 2.238F

h � 81.688 � 2.392T

h � 73.570 � 2.970H

h � 80.405 � 3.650R

Female

h � 61.412 � 2.317F

h � 72.572 � 2.533T

h � 64.977 � 3.144H

h � 73.502 � 3.876R


24. The costs C and income I for making and selling T-shirts with a schoollogo are given by the equations C = $535 + 4.50n and I = $12n,where n is the number of T-shirts.

a. How many T-shirts must be bought and sold to break even?Explain.

b. Suppose only 50 shirts are sold. Is there a profit or loss? Explain.

c. Suppose the income is $1,200. Is there a profit or loss? Explain.

d. i. For each equation, find the coordinates of a point that lies onthe graph of the equation.

ii. What information does this point give?

iii. Describe how to use the equation to see that the point will beon the graph.

25. The International Links long-distance phone company charges nomonthly fee but charges 18 cents per minute for long-distance calls.The World Connections long distance company charges $50 per month plus 10 cents per minute for long-distance calls. Compare the WorldConnections long-distance plan to that of International Links. Underwhat circumstances is it cheaper to use International Links? Explainyour reasoning.

26. Students at Hammond Middle School are raising money for theend-of-year school party. They decide to sell roses for Valentine’s Day.The students can buy the roses for 50 cents each from a wholesaler.They also need $60 to buy ribbon and paper to protect the roses aswell as materials for advertising the sale. They sell each rose for $1.30.

a. How many roses must they sell to break even? Explain.

b. How much profit is there if they sell 50 roses? 100 roses? 200 roses?




27. Ruth considers two different cable television plans. Company A has a cost plan represented by the equation CA = 32N, where N is the number of months she has the plan and CA is the total cost.Company B has a cost plan represented by the equationCB = 36 + 26N, where N is the number of months she is on the plan and CB is the total cost.

a. Graph both equations on the same axis.

b. What is the point of intersection of the two graphs? Whatinformation does this give us?

Connections28. Describe what operations are indicated in each expression, then write

each expression as a single number.

a. -8(4) b. -2 ? 4

c. 6(-5) - 10 d. 2(-2) + 3(5)

29. Decide whether each pair of quantities is equal. Explain.

a. 6(5) + 2 and 6(5 + 2) b. 8 - 3x and 3x - 8

c. 4 + 5 and 5 + 4 d. -2(3) and 3(-2)

e. 3 - 5 and 5 - 3 f. 2 quarters and 5 dimes

g. 1.5 liters and 15 milliliters

h. 2 out of 5 students prefer wearing sneakers to school and 50% ofthe students prefer wearing sneakers to school

30. a. Use your knowledge about fact families to write a related sentencefor n - (-3) = 30. Does this related sentence make it easier to find the value for n? Why or why not?

b. Write a related sentence for 5 + n = -36. Does this relatedsentence make it easier to find the value for n? Why or why not?

31. Write two different expressions to represent the area of each rectangle.

a. b.

7

x

1.5

5

4

x


32. Find each quotient.

a. b. c. d.

e. f. g.

33. Find the value of x that makes each equation true.

a. = b. =

c. = d. =

34. The sum S of the angles of a polygon with n sides is S = 180(n - 2).Find the angle sum of each polygon.

a. triangle b. quadrilateral c. hexagon

d. decagon (10-sided polygon)

e. icosagon (20-sided polygon)

35. Suppose the polygons in Exercise 34 are regular polygons. Find themeasure of an interior angle of each polygon.

36. How many sides does a polygon have if its angle sum is

a. 540 degrees b. 1,080 degrees

37. The perimeter of each shape is 24 cm. Find the value of x.

a. b.

c.

d. Find the area of each figure in parts (a)–(c).

2x 10

6

x

2

5x

34 x5

618

78 x

34 x3

12

343

12 x

2525

525

255

0210

21223

2123

1223




38. World Connections long-distance phone company charges $50 permonth plus 10¢ per minute for each call.

a. Write an equation for the total monthly cost C for t minutes of long-distance calls.

b. A customer makes hours of long-distance calls in a month. Howmuch is his bill for that month?

c. A customer receives a $75 long-distance bill for last month’s calls.How many minutes of long-distance calls did she make?

39. The number of times a cricket chirps in a minute is a function of thetemperature. You can use the formula

n = 4t - 160

to determine the number of chirps n a cricket makes in a minute whenthe temperature is t degrees Fahrenheit. If you want to estimate thetemperature by counting cricket chirps, you can use the following formof the equation:

t = + 40

a. At 608F, how many times does a cricket chirp in a minute?

b. What is the temperature if a cricket chirps 150 times in a minute?

c. At what temperature does a cricket stop chirping?

d. Sketch a graph of the equation with number of chirps on the x-axis and temperature on the y-axis. What information do the y-intercept and the coefficient of ngive you?

14 n

10 12


40. The higher the altitude, the colder the temperature. The formula T = t - is used to estimate the temperature T at different altitudes,where t is the ground temperature in degrees Celsius (Centigrade) and d is the altitude in meters.

a. Suppose the ground temperature is 0 degrees Celsius. What is thetemperature at an altitude of 1,500 meters?

b. Suppose the temperature at 300 meters is 26 degrees Celsius. Whatis the ground temperature?

41. As a person ages beyond 30, his or her height can start to decrease byapproximately 0.06 centimeter per year.

a. Write an equation that represents a person’s height h after the ageof 30. Let t be the number of years beyond 30 and H be the heightat age 30.

b. Suppose a 60- to 70-year-old grandmother is 160 centimeters tall.About how tall was she at age 30? Explain how you found youranswer.

c. Suppose a basketball player is 6 feet, 6 inches tall on his thirtieth birthday. About how tall will he be at age 80? (Remember, 1 inch < 2.54 centimeters.) Explain.

d150




Extensions42. The Small World long-distance phone company charges 55¢ for the

first minute of a long-distance call and 23¢ for each additional minute.

a. Write an equation for the total cost C of an m-minute long-distancecall. Explain what your variables and numbers mean.

b. How much does a 10-minute long-distance call cost?

c. Suppose a call costs $4.55. How long does the call last?

43. The maximum weight allowed in an elevator is 1,500 pounds.

a. The average weight per adult is 150 pounds, and the average weight per child is 40 pounds. Write an equation for the number of adults Aand the number of children C the elevator can hold.

b. Suppose ten children are in the elevator.How many adults can get in?

c. Suppose six adults are in the elevator.How many children can get in?

44. Solve each equation for x. Check your answers.

a. 5 - 2(x - 1) = 12

b. 5 + 2(x - 1) = 12

c. 5 - 2(x + 2) = 12

d. 5 - 2x + 2 = 12

45. Solve each equation for x. Explain what your answers might mean.

a. 2(x + 3) = 3x + 3 b. 2(x + 3) = 2x + 6

c. 2(x + 3) = 2x + 3


46. Wind can affect the speed of an airplane. Suppose a plane is flyinground-trip from New York City to San Francisco. The plane has acruising speed of 300 miles per hour. The wind is blowing from west toeast at 30 miles per hour.

When the plane flies into (in the opposite direction of) the wind, itsspeed decreases by 30 miles per hour. When the plane flies with (in thesame direction as) the wind, its speed increases by 30 miles per hour.

a. The distance between New York City and San Francisco is3,000 miles. Make a table that shows the total time the plane hastraveled after each 200-mile interval on its trip from New York Cityto San Francisco and back.

b. For each direction, write an equation for the distance d traveled in t hours.

c. On the same set of axes, sketch graphs of the time and distance datafor travel in both directions.

d. How long does it take a plane to fly 5,000 miles against a 30-mile-per-hour wind? With a 30-mile-per-hour wind? Explain how youfound your answers.

Distance (mi)

0

200

400

600

■

NYC to SF Time (h)

Airplane Flight Times

■

■

■

■

■

■

■

■

■

■

SF to NYC Time (h)



Date post:	02-Oct-2020
Category:	Documents
Upload:	others
View:	6 times
Download:	0 times

Applications - Pre-Algebra 8 and ATImrsdahlinmath.weebly.com/uploads/1/0/4/0/10405150/moving... ·...

Documents